Axisymmetric, stationary collisionless gas clouds trapped in a Newtonian potential

TL;DR

This paper models axisymmetric, stationary collisionless gas clouds around a massive object using Newtonian gravity, deriving key properties and comparing them to hydrodynamic models, with implications for astrophysical systems.

Contribution

It introduces models for collisionless gas clouds in a Newtonian potential, deriving macroscopic observables and analyzing their asymptotic behavior and physical properties.

Findings

Derived formulas for densities, pressure, and temperature.

Identified configurations with finite mass and energy.

Compared collisionless models with hydrodynamic analogs.

Abstract

The properties of an axisymmetric, stationary gas cloud surrounding a massive central object are discussed. It is assumed that the gravitational field is dominated by the central object which is modeled by a nonrelativistic rotationally-symmetric potential. Further, we assume that the gas consists of collisionless, identical massive particles that follow bound orbits in this potential. Several models for the one-particle distribution function are considered and the essential formulae that describe the relevant macroscopical observables, such as the particle and energy densities, pressure tensor, and the kinetic temperature are derived. The asymptotic decay of the solutions at infinity is discussed and we specify configurations with finite total mass, energy and (zero or non-zero) angular momentum. Finally, our configurations are compared to their hydrodynamic analogs. In an accompanying paper, the equivalent general relativistic problem is discussed, where the central object consists of a Schwarzschild black hole.